# Research: Background for Non-Physicists

When writing their theses, students in our group are asked to write an introductory chapter aimed at non-physicists. As Mike Boyer wrote in his, "I think it a good one [idea] because it allows me to provide to my friends and family at least a partial understanding as to how I have spent the past six years of my life." The below presentation is largely taken from his work.

# What do we do?

To sum up years of research in one sentence: we apply a technique known as scanning tunneling microscopy to the study of high-temperature superconductors in order to gain understanding of these materials on an atomic level.

The below sections will provide an elementary introduction to four subjects related to this research: conventional superconductors, applications of superconductors, high-temperature superconductors, and scanning tunneling microscopy. Our hope is that you (motivated non-physicists), will understand virtually all that is contained here.

# Conventional Superconductivity

Figure 1: A vertical peg board with stationary pegs (black circles). A blue disk falls and scatters through the lattice of pegs, analagous to electrons scattering off ions as they move through a wire, leading to resistivity.

Applying a voltage across a wire leads to an electric current in the wire. This electrical current has an analogy with a disk sliding down a board of organized pegs (Figure 1) made famous in the popular game "Plinko" seen on the game show The Price-is-Right. The moving disk is analogous to an electron moving through a lattice of ions (the pegs). The gravitational pull on the disk when the board is tilted (which leads to the disk falling through the array of pegs) is analogous to applying a voltage difference to move electrons through a material. As the disk falls through the array, the disk scatters off the pegs and slows down, in analogy with the way that electrons scatter off the ions in a material. The electron scattering events lead to a resistivity - an intrinsic property of the material related to the frequency of these scattering events which resist the flow of the electrons. Now, if we remove all the pegs, the disk will fall unimpeded. This unimpeded flow is exactly analogous to what happens when a material becomes superconducting - electrons no longer scatter. Some materials become superconducting below a critical temperature TC, which is different for each material. A material which becomes superconducting below a certain temperature TC has a resistivity which goes to zero below TC, and electrons flow unimpeded.

Figure 2. Initial data from Onnes's resistance measurements on mercury showing a precipitous fall in resistance around TC = 4.2 K

Zero resistivity below TC is the hallmark of superconductivity which was first discovered in 1911 by Kamerlingh Onnes for the element mercury below 4.2 K (Figure 2). Not surprisingly, this discovery occurred three years after Onnes first liquefied helium in 1908. The majority of conventional superconductors have critical transition temperatures TC below 10 K, and hence before the liquefaction of helium (boiling point of 4.2 K), there was no way to cool materials to cold enough temperatures to observe the superconducting phenomenon.

A second salient feature of superconductivity involves magnetic behavior known as the Meissner effect. When a magnetic field is applied over a superconductor at temperatures above TC, magnetic field lines penetrate directly through the material just as magnetic fields penetrate through any standard material such as paper or copper. However, when the material is cooled through TC and enters the superconducting state, magnetic field lines are expelled from the superconducting material (assuming a small enough magnetic field strength) (Figure 3). This is what is known as the Meissner effect. Although the initial resistive properties of superconductors were discovered in 1911, the Meissner effect was not discovered until years later in 1933 by Meissner and Oschenfeld.

Figure 3: a) Magnetic field lines penetrate through a superconductor at a temperature above its critical superconducting transition temperature (T > TC). b) When the superconductor is cooled below its critical transition temperature (T < TC), magnetic field lines are expelled from the interior of the superconductor due to the Meissner Effect.

The Meissner effect corresponds to perfect diamagnetism for small enough magnetic fields. Diamagnetism is a property of many materials; when an external magnetic field is applied to a diamagnetic material, the diamagnetic material sets up its own internal magnetic field to partially cancel the externally applied field. The diamagnetic properties of water have been shown through impressive demonstrations where strawberries and frogs have been levitated in air above strong magnets.(Figure 4)

Figure 4: a) A strawberry levitating in air in a strong magnetic field. The diamagnetic property of the water comprising the strawberry allows for this levitation. b) Similar to the strawberry, the frog contains enough water in its tissues to allow for its levitation in a strong magnetic field. c) Unlike the strawberry and the frog, the sumo wrestler is not levitated due to his composition of water. Instead, the sumo wrestler stands on a platform which is a strong permanent magnet disk. The cloth beneath the disk hides a superconductor cooled below its critical transition temperature. The sumo wrestler levitates due to the diamagnetic properties of the superconductor in the applied magnetic field of the disk platform. More information on these images available from HMFL. d) A conceptual way to visualize levitation and diamagnetism. If the one bar magnet represents the external field, the other magnet represents the diamagnetic response of a material where that material sets up a field in the opposite direction. We know there is a repulsive force between two bar magnets in this configuration. If the repulsive magnetic force is large enough to overcome the downwards gravitational pull on an object, then that object can levitate in air.

# Applications of Superconductivity

The macroscopic properties of superconductors have led to a number of applications - some in present use and some being developed for future use. Levitating strawberries and frogs are impressive but not particularly useful. However, superconductors are being used in the development of magnetic levitating trains, such as in the Yamanashi Maglev Test Line in Japan. The expectation is that trains will be able to reach higher speeds and utilize less energy if the trains move without friction - thus providing efficiency in travel time and energy usage. Utilizing superconducting wires with no resistance allows for the creation of "free" electromagnets. These magnets are free of the expense of supplying electrical power to the magnet, which power is now required for all large magnets made of resistive wire. Indeed, if one were to take a loop of superconducting wire and were to set a current flowing in this wire, it would continue to flow virtually forever. A study conducted in 1962 found that the time for dissipation was well over 100,000 years. This means is that, unlike for a copper wire, one would not have to have a battery continuously connected to the wire to maintain the flow of current. Combining several of these superconducting wire loops on top of one another, one can create an electromagnet. Today superconducting wire is used in the electromagnets of medical MRI (Magnetic Resonance Imaging) machines. Utilizing a property of superconductors we have not yet mentioned and will not touch in the rest of this thesis, superconductors can also be used to create very sensitive magnetometers with the ability to measure very small magnetic fields (of order 10-15 Tesla). To illustrate the impressive nature of this measurement, these small fields are 20 billion times smaller than the earth's magnetic field. These magnetometers have been used in Magneto encephalography (MEG) which studies the magnetic fields generated by the human brain. Finally, superconductors can be used to store energy efficiently. The demand on power stations varies significantly during the course of a day with the smallest demand during the late evening and early morning hours. If during the times when demand is smallest, power stations could generate and then store energy without any dissipation, this would lead to increased efficiency and significant savings. General Electric and other companies are currently studying and developing small versions of this energy storage known as Distributed Superconducting Magnetic Energy Storage (D-SMES). A few of these systems are used at present as the technology continues to be developed. It seems that further progress will be needed because there is still a high cost associated with cooling the present superconducting systems. The hope is eventually to create better superconductors which do not need to be cooled to very low temperatures. Superconducting technology would then become widely applicable.

# High Temperature Superconductivity

So far we have mentioned the salient macroscopic features of superconductivity (zero resistivity and the Meissner effect) as well as how those features can be used in technological applications. Both phenomenological and microscopic theories have provided insight into superconductivity. In 1957, Bardeen, Cooper, and Schrieffer formulated a microscopic theory of superconductivity (now known as BCS Theory) which could derive the macroscopic properties of superconductors starting from pairing of electrons below TC. Due to the successes of this theory, the scientific community generally viewed superconductivity as a well-understood phenomenon. However, in 1986, this all changed due to a new discovery. BCS theory had predicted a general restriction on the maximum possible critical temperature, TC, Max ~ 28 K. However, in 1986, Bednorz and Muller discovered a material (LaBaCuO) which enters the superconducting state below TC= 35 K, a temperature above the BCS-restricted maximum. This was the first of a new class of superconductors known as "high-temperature" superconductors. A critical temperature TC above the maximum TC set by BCS theory indicates that something different occurs on the microscopic level. To this date, the microscopic mechanism for these superconductors is not known. The purpose of this thesis is to garner additional insight into these high-temperature superconductors on a microscopic level with the ultimate aim that this research will lead to a microscopic theory for high temperature superconductors. Understanding high-temperature superconductors has important technological implications, both because of the higher transition temperatures as well as the ability to carry larger currents than wires of comparable size made out of copper. The higher transition temperatures mean that these superconductors can be cooled below their transition temperatures more easily than conventional superconductors. Liquid helium is the standard way to cool conventional superconductors below TC. Liquid helium is both expensive and not widely available. More recent high-temperature superconductors have TCs which are above 77 K, the boiling point of liquid nitrogen which is both widely available (for example in our breathable air) and inexpensive. The ability to push larger currents through high-temperature superconductors also has an advantage in terms of creating smaller wires as well as more powerful magnets.

# Scanning Tunneling Microscopy

Scanning tunneling microscopy (STM) is a powerful technique invented in 1981 by Binnig and Rohrer (Binnig et al. 1982). Because STM can probe materials on the atomic level, this technique naturally lends itself to the search for how high-temperature superconductors work on the microscopic level. The entirety of this thesis focuses on the application of STM to high-temperature superconductors and the insight this brings. This section is intended to give the non-physicist a glimpse of how STM works and the information it can provide.

Figure 5: A schematic STM setup. When a tip is brought several angstroms away from a sample and a voltage is applied between them, a very small current flows - of order 10-10 amperes - between the last atom of the tip and the sample. For comparison, a typical light bulb usually has a flowing current of order 1 ampere. Our tunneling current is roughly 10 billion times smaller. As we scan the tip over the surface, the rise and fall of the atomic landscape comprising the sample surface leads to changes in the current and hence to the STM's ability to image the surface (see Figure 6).

In STM, we bring an atomically sharp tip a few angstroms from an atomically flat surface. An angstrom (Å) is 10-10 meters, roughly the diameter of an atom. Applying a voltage between the tip and sample leads to a tunneling current flowing between the two (Figure 5). This current is very sensitive to the tip-sample distance. A larger distance between the tip and sample leads to a smaller current. A tip – sample distance change of about 1 Å leads to almost an order of magnitude change in the current, meaning that an STM is highly sensitive to very small changes in surface contours. Hence, as we scan the tip over a surface, the rises and falls in the surface topography (the rises and falls as we go over atoms) are easily captured.

Figure 6: A 70 Å-square scan taken by our custom-built STM over a material known as NbSe2. Here we see the triangular lattice composed of selenium atoms. NbSe2 is a superconductor below ~7.5 K and also exhibits another phenomenon known as charge density waves

Figure 7: A spectrum taken on the conventional superconductor Nb. The density of states is a measurement of how many electrons can reside at a specific energy level. In the figure, there are regions where no electrons can reside from ~ -1.5 mV to 1.5 mV. This is region is the superconducting energy gap. On either sides of this gap there are peaks in the density of states where large numbers of electrons can occupy the energy levels.

We are interested in studying this gap in the density of states of high-temperature superconductors, both as a function of position as well as of temperature. Because STM has atomic resolution, we can study how this gap changes from one atom to the next. Our STM has the ability to vary temperatures, and hence we can study how the density of states evolves with temperature both below TC and through TC. With the information from these studies, we gain insight into the superconducting state of high-temperature superconductors. The rest of this thesis will detail the experiments, results, and interpretations of these position- and temperature-dependent studies.